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# In a certain region V= $\;Axy+Bx^2+Cy\;$ where A , B , C are constants . Find electric field as a function of $\;(x ,y ,z)\;.$

$(a)\;(-Ay-2Bx)\;\hat{i}+(Ax+c)\;\hat{j}\qquad(b)\;(Ay+2Bx)\;\hat{i}+c\;\hat{j}\qquad(c)\;(Ay+2Bx)\;\hat{(-i)}+(Ax+c)\;\hat{(-j)}\qquad(d)\;None$

Answer : (c) $\;(Ay+2Bx)\;\hat{(-i)}+(Ax+c)\;\hat{(-j)}$
Explanation : $\;\overrightarrow{E}=-(\large\frac{\partial V}{\partial x}\;\hat{i}+\large\frac{\partial V}{\partial y}\;\hat{j}+\large\frac{\partial V}{\partial z}\;\hat{k})$
$\overrightarrow{E} = -(Ay+2Bx)\;\hat{i} + \;-(Ax+C) \;\hat{j} + 0 \;\hat{k}$
$\overrightarrow{E} = -(Ay+2Bx)\;\hat{i} -(Ax+C) \;\hat{j}$